The systems and methods described herein relate to magnetic resonance imaging (“MRI”) in general, and more particularly to a reconstruction method for sensitivity encoding with non-uniformly sampled k-space data.
Magnetic resonance imaging is a diagnostic imaging modality that does not rely on ionizing radiation. Instead, it uses strong (ideally) static magnetic fields, radio-frequency (“RF”) pulses of energy and magnetic field gradient waveforms. More specifically, MR imaging is a non-invasive procedure that uses nuclear magnetization and radio waves for producing internal pictures of a subject. Three-dimensional diagnostic image data is acquired for respective “slices” of an area of the subject under investigation. These slices of data typically provide structural detail having a resolution of one (1) millimeter or better.
Programmed steps for collecting data, which is used to generate the slices of the diagnostic image, are known as an MR image pulse sequence. The MR image pulse sequence includes magnetic field gradient waveforms, applied along three axes, and one or more RF pulses of energy. The set of gradient waveforms and RF pulses are repeated a number of times to collect sufficient data to reconstruct the slices of the image.
For image reconstruction, the collected k-space data are typically reconstructed by performing an inverse Fourier transform (IFT). However, in certain experimental settings, such as spiral acquisition techniques and non-rectilinearly sampled data, image reconstruction is not simple and artifacts, such as blurring due to off-resonance effects have to be corrected. Typically, a large number of 2D-FFTs have to be performed if the data set is large, which may cause impractical and unacceptable delays in image processing. Moreover, sensing coils employed in MR image acquisition can have different and complex sensitivity profiles, which may make reconstruction from non-uniformly sampled k-space data impractical or at least difficult.